Calculus Level 5

A certain road follows the path of a sine wave, with the equation $$y = \sin \left(\frac {\pi}{6} x\right)$$, whose origin represents the starting point of the road. If a car is travelling at this road starting at its origin, at an instantaneous speed of $$\frac { 9x^2}{3x^2 - 1} \sqrt{1+ \frac {\pi^2}{36}\cos^{2}\left( \frac{\pi}{6}x\right)}$$ m/s, as the car moves farther, determine the limiting rate (in m/s) as to how the car separates from the origin.

Note:

The values of $$x$$ and $$y$$ are in meters.

Clarification: In the graph above, the car follows the red path.

×